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I think by tone mapping he means the process of mapping a higher dynamic range to a lower display dynamic range. In the ACES system for example this is done in the RRT. So when he applies his creative LUTs he is not changing the color-space of the footage. He also explains this later in the text. Usually a print emulation LUT for example is converting from Cineon Log Printing Densities to DCI P3. His LUTs are comparable to LMTs in the ACES system. They are creative looks that can be applied in high dynamic range.

Probably there are some luma changes in these LUTs. Many looks depend on selective luma changes, for example changing the brightness in relation to the saturation and the hue.

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I think You have to get the 'LUT Translator' app for it. The template is a clean vector field. With the app any (non spatial) color operation that is applied to that image can be translated into a LUT.